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\frac{3x+9}{8},\frac{3x+10}{9},\frac{3x+11}{10},...,\frac{3x+49}{48} simplify

Source: Austrian Regional Competition For Advanced Students 2002 p1

January 11, 2020
simplifysimplificationnumber theoryminimum

Problem Statement

Find the smallest natural number x>0x> 0 so that all following fractions are simplified 3x+98,3x+109,3x+1110,...,3x+4948\frac{3x+9}{8},\frac{3x+10}{9},\frac{3x+11}{10},...,\frac{3x+49}{48} , i.e. numerators and denominators are relatively prime.
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